15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, 3 women do as much work as 2 men ?

Answer: Option D

3 women ≡ 2 men
So, 21 women ≡ 14 men
Less men, More days (Indirect proportion)
Less hours per day, More days (Indirect proportion)
$$\begin{array}{c}\text{Men 14}:15\text{hfill}\\ \text{Hours per day 6}:8\text{hfill}\end{array}\}::21:x$$
$$\begin{array}{rl}& \therefore \left(14\times 6\times x\right)=\left(15\times 8\times 21\right)\\ & \iff x=\frac{\left(15\times 8\times 21\right)}{\left(14\times 6\right)}\\ & \iff x=30\end{array}$$
∴ Required number of days = 30